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Look over onesignal
Personally I think that push notifications for a blog may be a bit spammy as a emailed newsletter should suffice. It's simple and has everything on one email, nothing too little while nothing too much. You could also just test out push notifications on your site and see what you think or how your users respond to it. If people respond well, then keep it, but if people don't like it, then remove it. Doesn't hurt to test out and see.
Also, even the people who are subscribed to your blog aren't always going to read it all of the time. If you have a decent following now, thats greats, but stay motivated and continue to post to you increase your following and then more people will read and engage with your blog.
Just stick with the newsletter. It’d take an immense amount of trust for someone to want to receive push notifications.